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The Kings that we come across in Sophocles' 'Antigone' and Euripides 'Medea' display qualities which are quite far from kingly ideals and in fact exhibit thoughts and action against the spirit of ideal kingship. Creon and Aegeus in 'Medea' behave without discretion and judgement and pursuing selfish personal goals endanger not just themselves but also their entire state. Creon in 'Antigone' suffers from an egotism which makes him endanger the moral climate of his state and incur the wrath of the Gods on his family. In contrast the protagonists come across as more heroic, showing courage, ingenuity, resolve and determination beyond those expected of their gender.
The two Creons from Antigone and Medea have displayed kingship styles which are very different from each other. In Antigone, Creon in his first monologue appears to adhere staunchly to the state laws (laws made by the king or his predecessors) and does what he feels is best without looking at whether the gods accept his beliefs or not; "the power of the throne is eternal".  He says "a man who thinks more highly of a friend than his country, well, he means nothing to me"  which goes to show if given a choice between friends and country like a noble king he says country. He is autocratic-"I have the throne, all royal power".  In his interchange with the Guard he reveals himself to be impatient and immature as even the guard got him irritated- "but I find your voice so irritating-don't you realize that?"  He talk's highly about justice [quote] but his actions reveal him to be unjust. He threatens the guard, "unless you bring him here before my eyes, then death for you will never be enough. No, not before you're hung up still alive".  He accuses and wants to punish Ismene without a trial - "not escape my harshest punishment - her sister, too".  He takes decisions which backfire such as putting Antigone to death. Creon feels that to assert power and authority he must administer punishment or he'll be seen as weak- "well, in this case, if she gets her way and goes unpunished, then she's the man here, not me". 
Creon, in Medea, does not even claim to hold the State as important. He isn't an ideal ruler as he values his children's interests over those of the state, "I love my country too-next after my children".  In his interchange with Medea he starts off with aggressively attacking Medea who has just earlier received the sympathy from the Nurse and the Chorus for her pathetic condition after Jason's betrayal- "you, with that angry look, so set against your husband, Medea, I order you to leave my territories".  He doesn't think of the rights of Medea's children and only wants his daughter to be safe and exiles Medea and her children revealing him to be cruel and heartless. Creon accepts that he is scared of Medea and her superhuman powers- "I am afraid of you-why should I dissemble it?"  admitting to cowardice not suitable in a king. Creon banishes Medea and says "it is my decree, and I will see it done. I will not return home until you are cast from the boundaries of my land".  He goes on to say "you will never persuade me".  And then in an act of incomprehensible foolishness he gets taken in by Medea's deceptions even after being aware of her cleverness. He displays irresponsible leadership and abdication of all his duties as a King.
The guard in Antigone exposes Creon's shortcomings through his comments on Creon. The guard anticipated Creon's reaction to the news of the burial of Polyneices body and manipulates Creon and delays his punishment successfully. It is seen how the minor ranked character corrects the major character-- "how strange and sad when the one who sorts this out gets it all wrong".  He irritates Creon and fearlessly asks him what hurts more -"where does it hurt? Is it in your ears or in your mind."  His long dialogue with his King irritates and tires the King so much that Creon wants Antigone to describe her role in the burial "briefly-not in some lengthy speech".  However it is Teiresias, a blind prophet whose prophecies never turn out to be wrong who reveals the complete falseness of Creons' position-"I'll tell you and you obey the prophet".  He also represents the authority of religion which rivals Creon's authority-"I know-thanks to me you save the city and now are in control"  . He brings out loopholes in Creon's character even as his entry is the turning point of the play. He talks to him in a very confident and superior manner and as a result Creon's ego is affected. Creon's disrespect to him reveals his vanity and ego but which is corrected by his dire prophecy and the caution of the Chorus-"Yes, my lord, as fast as possible. Swift footed injuries sent from the Gods hack down those who act imprudently." 
Aegeus' introduction is significant primarily in terms of plot when seeing his desperation for children she sees in the death of her own children an unparalleled opportunity for revenge against Jason. She has also got a safe haven from Aegeus where she may escape and live in exile. He seems comparably more admirable than King Creon. Aegeus appears to be smarter than Creon from the outset as he allows her a safe haven but on a condition that she by herself can reach his house. Again he stops short of being the complete courageous hero; he does not provide unconditional help especially as he feels she has been wronged - "does Jason consent? I cannot approve of this."  Again he arrives at this judgement without any deep probe of the matter hearing only Medea's side of the story. He is in such a hurry to procure Medea's help that he allows her to set the terms of agreement swearing on all the Gods Medea mentions. It should not be forgotten that in both the plays, Medea and Antigone, kingship is being somewhat linked with selfishness. Both the Creons and even Aegeus in Medea have personal goals to achieve during their monarchical rule. A childless Aegeus is an impotent King and like Creon in Medea is out to ensure a successor. To that extent they are willing to compromise: Creon will unjustly and heartlessly evict Medea and her children after stealing her husband from her for his daughter; Aegeus will compromise the security of his state by getting a sorceress with a violent past into his country and risk annoying his allies in Corinth and Creon in Antigone bullies his inferiors, the chorus, the guard, Antigone, Ismene, Haemon and is ready to revoke the same laws which he had used to mutilate Polyneices body and order Antigone's execution when he wants to save his own son and family.
Creon who doesn't respect people "who thinks more highly of a friend than his country"  later demands from Haemon obedience due to a father than as a king hence going against his own belief-"You're the worst there is-you set your judgement up against your father".  He says -"don't yield to those who contravene my orders"  but he himself rolls back his own death penalty that he had announced on Antigone. Their speeches in Medea and Antigone echo with irony. They show that how the two were over confident and underestimated the rest. In Medea, Creon underestimates that Medea cannot do anything in one day and in Antigone he says that women themselves cannot do anything.
Antigone is unrepentant, audacious and fearless and continues to do what she feels is right that is to go by the divine laws and ridicules Creon's so-called 'state laws'-"Yes. Zeus did not announce those laws to me. And Justice living with the gods below sent no such laws for men."  She isn't worried about the punishment she is going to receive from Creon as she has the self-confidence and faith in her holy cause. Medea's cause is the opposite of holy but her unwavering vengeance against Jason as well as her skills and resourcefulness that help her to outwit Creon by begging him by his "knees"  and by his "newly wedded girl"  and that help her manipulate Aegeus - two kings - comes across as impressive.
Both Creons suffer the same end - one dies trying to save his fatally poisoned daughter and the other is reduced to a "breathing corpse"  after the deaths of his wife and son. They seem to have no existence outside the sphere of the self and the family whereas Antigone's readiness to sacrifice self; her courage, valour and spirit and her unquestionable dominion over the moral kingdom shows her stature. Medea's intelligence, Machiavellian statesmanship, diplomatic negotiation and strategising exposes the lack of these qualities in the Kings of the plays. Both playwrights have succeeded in banishing the palace from centre stage allowing for new heroines to come up.